Yoshihiro Hayashiuchi

A new interpretation of proportionality between vacancy formation energy and melting point

A simple picture of vacancy formation in pure metals is proposed to account for the empirical law that the vacancy formation energy W is proportional to the melting point Tm. We imagined that surface vacancy is created by making a transition of a surface atom from a solid state to a liquid one. Thus W becomes equivalent to the transition energy of the atom to a liquid state. If one creates the concentrated liquid state atoms by depositing an energy e on a surface spot. W is nearly given by e divided by the number of liquid state atoms n. For large n, this process could be pictured as a melting of the surface spot. Determining n by the thermal spike model for the energy e, we found a constant W/kTm = 3(3/4π)(2πe/3)32 = 9.7, k being Boltzmanns constant. This value is in good agreement with the empirical one.